@article{29e0e8d169744acc9fe144b8cc8b8bc1,
title = "Variational Phase Retrieval with Globally Convergent Preconditioned Proximal Algorithm",
abstract = "We reformulate the original phase retrieval problem into two variational models (with and without regularization), both containing a globally Lipschitz differentiable term. These two models can be efficiently solved via the proposed Partially Preconditioned Proximal Alternating Linearized Minimization (P3ALM) for masked Fourier measurements. Thanks to the Lipschitz differentiable term, we prove the global convergence of P3ALM for solving the nonconvex phase retrieval problems. Extensive experiments are conducted to show the effectiveness of the proposed methods.",
keywords = "Global convergence, Partially preconditioned proximal alternating linearized minimization, Phase retrieval, Poisson/Gaussian noise, Regularization, Total variation, Variational model",
author = "Huibin Chang and Stefano Marchesini and Yifei Lou and Tieyong Zeng",
note = "Funding information: The work of the first author was partially supported by the National Natural Science Foundation of China (11501413, 11426165, and 51609259), the China Scho l arship Council (CSC), 2017-Outstanding Young Innovation Team Cultivation Program 043-135202TD1703, Young Backbone of Innovative Personnel Training Program 043-135205GC37, and Innovation Project 043-135202XC1605 of Tianjin Normal University. The work of the third author was partially supported by NSF grant DMS-1522786. The work of the fourth author was partially supported by NSFC 11271049 and RGC 12302714. This work was also p artially funded by the Center for Applied Mathematics for Energy Research Applications, a joint ASCR-BES funded project within the Office of Science, US Department of Energy, under contract DOE-DE-AC03-76SF00098. Publisher copyright: {\textcopyright} 2018, Society for Industrial and Applied Mathematics",
year = "2018",
month = jan,
day = "11",
doi = "10.1137/17M1120439",
language = "English",
volume = "11",
pages = "56--93",
journal = "SIAM Journal on Imaging Sciences",
issn = "1936-4954",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "1",
}